My main text when reading the T'ai Chi Classics is Waysun Liao's translation, and although I haven't seen a reference in it to "The Four Polarities" -- maybe I missed it -- it translates the eight powers as ward off power (pong jing), push power (on jing), rollback power (lui jing), press power (ji jing), roll-pull power (tsai jing), split power (leh jing), elbow power (dzo jing) and lean forward power (kao jing).

Oh... different "8 powers". You get a lot of different things with the magic numbers of 2, 4, 8, 16, 32, 64, etc.

The ones I was referring to are the ones that Stevens translated in relation to references made by O-Sensei and they're a standard "poem" that has to do with the development of qi power and how you exercise it.

The 8 things you're referring to are part of the so-called "13 Postures" of Taiji, although there is some discussion about what comprises the last 5. The important part of the 8 you're quoting is the peng, lu, ji, an (the other 4 are considered auxilliaries or maybe "emergency techniques" that still use the first 4 powers). Peng, lu, ji, and an are the basic directional powers of kokyu and mean basically kokyu up, toward the body, away from the body, and downward. For instance, if Tohei is standing to that people cannot lift him easily (or conversely he is applying power downward), he is demonstrating "an" power. If Tohei is resisting a push to his forearm or if he is pushing someone away, he is using "ji" power (as long as it is the correct, relaxed, solid power). And so on. Using the 4 directions of power you can describe any motion you make. E.g., to extend your arm in front and move it in a circle, to do it correctly, it will be powered with all 4 of peng, lu, ji, an. Since the middle is between the arm and the foot and because the middle, not the shoulder, directs those powers, you automatically "move from the center", etc.

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The Yang long form as taught by T. T. Liang is what I study, incidentally.

Taiji uses the same basic power that Aikido is supposed to use. In both cases, many (if not most) practitioners think the secret is in the forms and techniques, but it's actually in how you move. I agree with Tohei on that one.